Liquid-cooling using microchannel heat sinks etched on silicon dies is seen as a promising solution to the rising heat fluxes in two-dimensional and stacked three-dimensional integrated circuits. Development of such devices requires accurate and fast thermal simulators suitable for early-stage design. To this end, we present 3D-ICE, a compact transient thermal model (CTTM), for liquid-cooled ICs. 3D-ICE was first advanced incorporating the 4-resistor model-based CTTM (4RM-based CTTM). Later, it was enhanced to speed up simulations and to include complex heat sink geometries such as pin fins using the new 2 resistor model (2RM-based CTTM). In this paper, we extend the 3D-ICE model to include liquid-cooled ICs with multi-port cavities, i.e., cavities with more than one inlet and one outlet ports, and non-straight microchannels. Simulation studies using a realistic 3D multiprocessor system-on-chip (MPSoC) with a 4-port microchannel cavity highlight the impact of using 4-port cavity on temperature and also demonstrate the superior performance of 2RM-based CTTM compared to 4RM-based CTTM. We also present an extensive review of existing literature and the derivation of the 3D-ICE model, creating a comprehensive study of liquid-cooled ICs and their thermal simulation from the perspective of computer systems design. Finally, the accuracy of 3D-ICE has been evaluated against measurements from a real liquid-cooled 3D-IC, which is the first such validation of a simulator of this genre. Results show strong agreement (average error < 10%), demonstrating that 3D-ICE is an effective tool for early-stage thermal-aware design of liquid-cooled 2D-/3D-ICs.